To spin the game out longer I've been doing a lot of hunting tasks and really enjoyed the journey on acquiring the legend of the east satchel which massively improves satchel space. The last part of this task involves getting a perfect cougar pelt which turned out to be a bit of a pain for me.
If you're hunting cougars head for the location on this part of the map. When you get there don't go to the illustration of the cougar on the map, or start meandering around in the woods, but keep travelling back and forth alongside the path at the side of the river. If you don't find one after a few attempts set up camp and try again. At first I hitched my horse and did this on foot and for some reason didn't encounter any cougars at all, so do this on your horse to increase your chances of finding one. If you've not encountered a cougar before they hit hard and fast, giving little notice of their presence or time to react to it. The good news is that their attack style is usually jumping at you in attempt to rip off your face, running off and coming straight back for another go at you. This gives you time ready your weapon and dead eye that beast. I found that there were more opportunities to find them in the mornings too. Finally, I personally didn't bother with predator bait which I find to be pretty ineffective in all circumstances.